Perfect for Parties: The Great Birthday Riddle

By Rachel Mount Hofstetter

Quick: take a fast guess at this dinner party-worthy math problem. How many people would I have to invite to my party if I wanted a 50 percent chance that two people would have the same birthday? 366 people would give me a 100 percent chance, but what about a 50 percent chance?

I guessed 100.

It turns out, thanks to the magic of probability, that you’d only need 23 people. In that case, there’s a 50/50 chance two people’s birthdays would match. The math isn’t nearly as complicated as it might seem—you can read the whole analysis here via the New York Times. Then you can pose the riddle at dinner—and watch everyone’s eyes widen.